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This is how I take it; υ is long in χρῡ́σεος and short in λήκυθος. -σέηι is just one long syllable, because of synizesis. ωι is short in ληκύθωι, because of correption - long vowels are regularly shortened at the end of the word, if the next word starts with a vowel.

I continued with the rest of the poem in wikipedia and it was a nice surprise to see that I have already known almost all the words from Homer. And I like it very much, may be it would be a great option to read after Homer.

There's not much of Mimnermus left--just one or two longer fragments and a number of shorter ones. But It would be worthwhile for everyone interested in Homer and archaic Greece to read through the main fragments of the lyric, elegiac and iambic poets in Campbell's book:

This book collects most of the important fragments, with helpful notes:

There isn't much of this, since for the most part, it's entirely fragmentary, with a few complete poems, and it shouldn't take long to work through the book. Campbell is also responsible for the new Loeb collection, in multiple volumes.

The vocabulary of Greek elegy is essentially the vocabulary of the Homeric poems--and even Tyrtaeus, the Spartan poet, composed elegies in Ionic.